Optimal sorting of product into fixed weight packaging

Compac Sorting Equipment make very nifty machines for sorting fruit by weight, diameter, colour, density, blemish or even shape. Compac sought solutions to two closely related problems: the boxing problem and the bagging problem. The boxing problem requires graded fruit to be assigned to outlets where boxes are filled with a specified number of fruit to a minimum weight (and a specified tolerance for underweights). The aim is to maximise the number of boxes packed. The decision must be made after all information is known, but before the fruit passes the first outlet - a few seconds total. Further, information about fruit already packed in a given box is incomplete (we don’t know exactly which fruit ended up in a box). The bagging problem requires bags to be filled to a minimum weight - no tolerance for underweights, and no constraints on the number of fruit per bag. In this case complete information is available on fruit already assigned to a bag. Again the aim is to maximise the number of bags packed

Multipoint-to-multipoint network communication

We have formulated an exact ILP model for the problem of communicating on a virtual network. While this ILP model was successful in solving small problems, it is not recommended to handle larger instances, due to the fact that the number of variables in the model grows exponentially as the graph size grows. However, this ILP model can provide a benchmark for heuristic algorithms developed for this problem. We have also described a heuristic approach, and explored several variants of the algorithm. We found a solution that seems to perform well with reasonable computation time. The heuristic is able to find solutions that respect the degree constraints, but show a small number of violations of the desired time constraints. Tests on small problems show that heuristic is not always able to find feasible solutions, even though the exact method has shown they exist. It would be interesting in the future to look at whether insights gained by looking at exact solutions can be used to improve the heuristic

Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Solving the Integrated Bin Allocation and Collection Routing Problem for Municipal Solid Waste: a Benders Decomposition Approach

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent, i.e., the solution to one of the problems restricts the solution to the other, they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bah\'{i}a Blanca, Argentina, showing smaller computing times than solving a full MIP model.Comment: 29 pages, 6 figure

Dynamic scheduling of recreational rental vehicles with revenue management extensions

The rental fleet scheduling problem (RFSP) arises in vehicle-rental operations that offer a wide variety of vehicle types to customers, and allow a rented vehicle to migrate to a setdown depot other than the pickup depot. When there is a shortage of vehicles of a particular type at a depot, vehicles may be relocated to that depot, or vehicles of similar types may be substituted. The RFSP involves assigning vehicles to rentals so as to minimise the costs of these operations, and arises in both static and online contexts. The authors have adapted a well-known assignment algorithm for application in the online context. In addition, a network-flow algorithm with more comprehensive coverage of problem conditions is used to investigate the determination of rental pricing using revenue management principles. The paper concludes with an outline of the algorithms use in supporting the operations of a large recreational vehicle rental company

Bi-Objective Search with Bi-Directional A*

Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control in energy systems. Recently, bi-objective A*-based search (BOA*) has shown state-of-the-art performance in large networks. This paper develops a bi-directional and parallel variant of BOA*, enriched with several speed-up heuristics. Our experimental results on 1,000 benchmark cases show that our bi-directional A* algorithm for bi-objective search (BOBA*) can optimally solve all of the benchmark cases within the time limit, outperforming the state of the art BOA*, bi-objective Dijkstra and bi-directional bi-objective Dijkstra by an average runtime improvement of a factor of five over all of the benchmark instances

Vehicle Dynamics in Pickup-And-Delivery Problems Using Electric Vehicles

Electric Vehicles (EVs) are set to replace vehicles based on internal combustion engines. Path planning and vehicle routing for EVs need to take their specific characteristics into account, such as reduced range, long charging times, and energy recuperation. This paper investigates the importance of vehicle dynamics parameters in energy models for EV routing, particularly in the Pickup-and-Delivery Problem (PDP). We use Constraint Programming (CP) technology to develop a complete PDP model with different charger technologies. We adapt realistic instances that consider vehicle dynamics parameters such as vehicle mass, road gradient and driving speed to varying degrees. The results of our experiments show that neglecting such fundamental vehicle dynamics parameters can affect the feasibility of planned routes for EVs, and fewer/shorter charging visits will be planned if we use energy-efficient paths instead of conventional shortest paths in the underlying system model